Solve (13/99+33/33+95/11)div(1/99+3frac{1}{33}+9frac{1}{11})

$$( 1 \frac { 3 } { 99 } + \frac { 33 } { 33 } + \frac { 95 } { 11 } ) \div ( \frac { 1 } { 99 } + 3 \frac { 1 } { 33 } + 9 \frac { 1 } { 11 } )$$

Evaluate

$$\frac{1056}{1201}\approx 0.879267277$$

Solution Steps

Divide 33 by 33 to get 1.

$$\frac{\frac{1\times 99+3}{99}+1+\frac{95}{11}}{\frac{1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Multiply 1 and 99 to get 99.

$$\frac{\frac{99+3}{99}+1+\frac{95}{11}}{\frac{1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Add 99 and 3 to get 102.

$$\frac{\frac{102}{99}+1+\frac{95}{11}}{\frac{1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Reduce the fraction \frac{102}{99} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{34}{33}+1+\frac{95}{11}}{\frac{1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Convert 1 to fraction \frac{33}{33}.

$$\frac{\frac{34}{33}+\frac{33}{33}+\frac{95}{11}}{\frac{1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Since \frac{34}{33} and \frac{33}{33} have the same denominator, add them by adding their numerators.

$$\frac{\frac{34+33}{33}+\frac{95}{11}}{\frac{1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Add 34 and 33 to get 67.

$$\frac{\frac{67}{33}+\frac{95}{11}}{\frac{1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Least common multiple of 33 and 11 is 33. Convert \frac{67}{33} and \frac{95}{11} to fractions with denominator 33.

$$\frac{\frac{67}{33}+\frac{285}{33}}{\frac{1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Since \frac{67}{33} and \frac{285}{33} have the same denominator, add them by adding their numerators.

$$\frac{\frac{67+285}{33}}{\frac{1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Add 67 and 285 to get 352.

$$\frac{\frac{352}{33}}{\frac{1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Reduce the fraction \frac{352}{33} to lowest terms by extracting and canceling out 11.

$$\frac{\frac{32}{3}}{\frac{1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Multiply 3 and 33 to get 99.

$$\frac{\frac{32}{3}}{\frac{1}{99}+\frac{99+1}{33}+\frac{9\times 11+1}{11}}$$

Add 99 and 1 to get 100.

$$\frac{\frac{32}{3}}{\frac{1}{99}+\frac{100}{33}+\frac{9\times 11+1}{11}}$$

Least common multiple of 99 and 33 is 99. Convert \frac{1}{99} and \frac{100}{33} to fractions with denominator 99.

$$\frac{\frac{32}{3}}{\frac{1}{99}+\frac{300}{99}+\frac{9\times 11+1}{11}}$$

Since \frac{1}{99} and \frac{300}{99} have the same denominator, add them by adding their numerators.

$$\frac{\frac{32}{3}}{\frac{1+300}{99}+\frac{9\times 11+1}{11}}$$

Add 1 and 300 to get 301.

$$\frac{\frac{32}{3}}{\frac{301}{99}+\frac{9\times 11+1}{11}}$$

Multiply 9 and 11 to get 99.

$$\frac{\frac{32}{3}}{\frac{301}{99}+\frac{99+1}{11}}$$

Add 99 and 1 to get 100.

$$\frac{\frac{32}{3}}{\frac{301}{99}+\frac{100}{11}}$$

Least common multiple of 99 and 11 is 99. Convert \frac{301}{99} and \frac{100}{11} to fractions with denominator 99.

$$\frac{\frac{32}{3}}{\frac{301}{99}+\frac{900}{99}}$$

Since \frac{301}{99} and \frac{900}{99} have the same denominator, add them by adding their numerators.

$$\frac{\frac{32}{3}}{\frac{301+900}{99}}$$

Add 301 and 900 to get 1201.

$$\frac{\frac{32}{3}}{\frac{1201}{99}}$$

Divide \frac{32}{3} by \frac{1201}{99} by multiplying \frac{32}{3} by the reciprocal of \frac{1201}{99}.

$$\frac{32}{3}\times \frac{99}{1201}$$

Multiply \frac{32}{3} times \frac{99}{1201} by multiplying numerator times numerator and denominator times denominator.

$$\frac{32\times 99}{3\times 1201}$$

Do the multiplications in the fraction \frac{32\times 99}{3\times 1201}.

$$\frac{3168}{3603}$$

Reduce the fraction \frac{3168}{3603} to lowest terms by extracting and canceling out 3.

$$\frac{1056}{1201}$$

Factor

$$\frac{2 ^ {5} \cdot 3 \cdot 11}{1201} = 0.8792672772689425$$